# Centering and scaling skewed distributions

I have a dataset where the features are skewed (non normal) distributions. My preprocessing pipeline consists of the following steps:

1. Missing values imputation
2. Centering and scaling (zero mean and unit variance) of each feature
3. Transforming the features to an approximate normal distribution by using the Box-Cox Transformation.

Should I first do the centering and scaling or the transformation?

Second, if the distributions are skewed (not normal) is centering and scaling (zero mean and unit variance) still ok? Another possiblity would be to subtract the median (instead of the mean) and dividing by 1.5 * the interquartile range (instead of the standard deviation).

• Depends on your Box-Cox machinery, but I don't know how you consider transformations such as logarithm and square root which are, apart from extra constants, members of the Box-Cox family if your variable has negative values, as it will after standardization. In short, #2 cannot precede #3 without correction. Apart from that, linear transformations such as (value $-$ summary) / spread have precisely no effect on skewness and kurtosis. Note that non-normal is not a synonym for skewed as there are symmetric distributions that aren't normal (and which could be awkward for data analysis). – Nick Cox Mar 21 '16 at 23:56